<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: LPSPACE1:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">V1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">V1</font> is  <a href="rlsub_1.html#V1" title="RLSUB_1:attr.1">linearly-closed</a>  iff ( <font color="Olive" title="b2">V1</font> is  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>  &amp; <font color="Olive" title="b2">V1</font> is  <a href="lpspace1.html#V1" title="LPSPACE1:attr.1">multi-closed</a>  ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_1.html#D1" onmouseover="rs('rlsub_1/D1')" onmouseout="rh()">RLSUB_1:def 1</a></span>;<br/></div></div>
